1. Business F723 Fixed Income Analysis Week 5 Liability Funding and Immunization

2. 2 Institutional Investors Investment strategies and planning horizon dictated by nature of their liabilities Liability funding strategy to set cash flows from assets = cash flow to liabilities Basic principal; to minimize risk, set the duration of assets = duration of liabilities Bad example: US Savings & Loan collapse

3. 3 Types of Institutions Depository Institutions; in the Spread Banking business, make money on spread between assets and liabilities (banks, ins.) Pension funds; try to cover defined benefits at minimum cost Mutual funds and others; no fixed liabilities, try to generate maximum return

4. 4 Types of Liability Type 1; certain in time and amount; GIC Type 2; certain in amount but not time –Life insurance policy Type 3; certain time in but not amount Type 4; certain in neither time nor amount –Auto insurance policy

5. 5 Liquidity Concerns If cash flows to liabilities are uncertain, liquidity becomes a serious concern –GIC: early withdrawal with penalty –Life insurance; cash surrender or loan value –Mutual funds; net disposals

6. 6 Asset/Liability Management Two primary goals of financial institutions –Earn a reasonable return on investment –Maintain a surplus of assets over liabilities, also called Surplus Management Trade-off between risk and return Risk must be measured for both assets and liabilities

7. 7 Types of Surplus Economic Surplus; present value of assets in excess of the present value of liabilities Accounting Surplus; as specified by GAAP Regulatory Surplus; as specified by various regulatory bodies charged with protecting the stakeholders in various institutions

8. 8 Economic Surplus Best from a finance standpoint Surplus = PV Assets - PV Liabilities If duration of the assets and liabilities are not the same, a change in interest rates can change the value of the surplus e.g. $10 million assets, duration 10 $9.2 million liabilities, duration 15 what happens with a 1% decrease in YTM?

9. 9 Accounting Surplus Financial reporting according to GAAP, FASB 115 in USA –Amortized cost (book value) –Market value –Lower of cost or market Which method is allowed depends on what the institution intends

10. 10 FASB 115

11. 11 Regulatory Surplus Uses Regulatory Accounting Principals (RAP) no overall guiding rules, each jurisdiction and regulatory body is free to determine the rules that the financial institution must follow for reporting to the regulatory body

12. 12 Immunization Defined by F. M. Reddington in 1952 –The investment of the assets in such a way that the existing business is immune to a general change in the rate of interest For funding a single liability, consider 3 bonds and a liability of $2,091.23 due in 8 years

13. 13 The 8-year, 10% Bond

14. 14 The 8-year, 10% Bond

15. 15 The 20-year, 7.5% Bond

16. 16 The 20-year, 7.5% Bond

17. 17 The 14-year, 12% Bond

18. 18 The 14-year, 12% Bond

19. 19 Why? Duration of the 3 bonds (Macauly’s, modified duration would be similar since YTM is constant) –The 8-year, 10% Bond = 5.827 –The 14-year, 12% Bond = 7.998 –The 20-year, 7.5% Bond = 10.425 A bond with a duration equal to the duration of the liability will have offsetting price and reinvestment risks

20. 20 Multiple Bonds Set portfolio duration equal to duration of obligation That gives 52.74% of the funds in bond A and 47.26% of the funds in bond C

21. 21 Multiple Bonds

22. 22 Portfolio

23. 23 Rebalancing a Portfolio What is the duration of an investment in the 8-year, 10% Bond, six months later, if the YTM is now 7.5%? Note: duration of cash = zero

24. 24 Rebalancing Considerations As time passes and interest rates change, the duration of an immunized portfolio can drift away from the target duration Buying and selling bonds can bring the duration back to the target, but will give rise to transaction costs Frequent rebalancing can be expensive, but it will reduce the risk from duration drift

25. 25 Immunization Risk Since duration measures the approximate change in price for a parallel change in the yield curve, duration matching leaves some risk in an immunized portfolio Fong and Vasicek developed a measure of immunization risk

26. 26 Immunization Risk Calculate the immunization risk for the 12%, 14-year bond at a YTM of 8%, given a horizon of 8 years

27. 27 Immunization Risk Calculate the immunization risk for the portfolio at a YTM of 8%, given a horizon of 8 years

28. 28 Zero-Coupon Bonds From the immunization risk measure (or just by intuition) we can see that a pure discount bond maturing on the date of the obligation has no immunization risk Unfortunately, in practice, the zero-coupon bond has a lower yield than coupon bonds This leads to another risk/return trade-off

29. 29 Credit Risk and Target Yield If one or more of the bonds in the portfolio defaults or suffers a downgrade, the target yield may not be realized The tactic to minimize this risk is to restrict the allowable bonds to those with a level of credit risk with which the client is comfortable Similar to the zero-coupon problem this brings up another risk/return trade-off

30. 30 Call Risk If any of the bonds in the portfolio are callable, this will increase the risk that the target value will not be reached Restricting bonds to those which are not callable or are trading at a deep discount will reduce the level of call risk… and the expected return on your investment

31. 31 Building the Portfolio After deciding on the allowable bonds, build a portfolio that matches the duration of the obligation Mathematical tools can be used to minimize the objective function, which is often the immunization risk measure Alternatively, this can be done by matching both duration and convexity

32. 32 Contingent Immunization A strategy where a safety net return is lower than that currently available is acceptable This allows the fund manager to pursue an active trading strategy to seek higher yields If the portfolio value drops to a point where there is no safety cushion, then the strategy will change to immunization

33. 33 Multiple Liabilities If there are multiple liabilities in the future, the duration matching condition is still valid but extra conditions must also be satisfied The distribution of durations of the assets must be wider than that of the liabilities The present value of the portfolio must equal the present value of the liabilities

34. 34 Multiple Liabilities As with single liability immunization, the portfolio is only protected against parallel shifts in the yield curve Fong and Vasicek’s immunization risk measure can be used in this case too Immunization strategies for one type of non-parallel shift can increase the risk from a different non-parallel shift

35. 35 Cash Flow Matching Multiple liabilities can be hedged by creating a portfolio where the cash inflows are equal to the required cash outflows This can be done by matching the final required cash flow to that of a bond’s final payment, the next to last payment can be covered by the previous bond’s coupon plus the final payment of another bond, etc.

36. 36 Cash Flow Matching Example You are required to pay $2m every six months for the next 3 years Construct a bond portfolio to fund this obligation

37. 37 Combining Active and Immunization Strategies A mixed strategy of actively managing part of the portfolio and actively managing the rest of the portfolio